Meeting Report: Norris Address
Bursting Bubbles
Richard N. Zare
Department of Chemistry
Stanford University, Stanford, CA 94305-5080
Xun Zi (about 313 – 238 BC), a follower of Confucius, wrote:
Roughly translated it means: “I hear
and I forget, I see and I remember, I do
and I understand.” It seems that handson learning was highly appreciated
long before modern educators made
this phrase so popular. This time-honored insight inspired this year’s Norris
Lecture, which was titled “Chemical
Fizzics.” True to its name, the lecture
treated the audience to numerous
demonstrations on bubbles, foam,
froth, and fizz. Once again, the outcome of a lecture demonstration that
contradicts prior conceptions proves to
be most memorable. Moreover, such
demonstrations can also be both
enlightening and entertaining. Space
constraints do not allow a full description of all the fizzics covered in this
lecture 1 – why bubbles grow as they
rise in a carbonated beverage, why
bubbles in some carbonated beverages
fall along the sides of the container as
the beverage settles, and why women
often leave less foam in a glass of
champagne or a mug of beer than men
do. One example might serve to give
the flavor of what was presented.
Consider the life cycle of a bubble
in a pot of water that is brought to a
boil. Bubbles first form on the sides
and bottom of the container, lift off
when large enough, rise to the surface,
and pop. Why are no bubbles formed
inside the liquid? Why do bubbles
only appear on the container’s walls,
often in places that have been nicked
or scratched? This phenomenon is an
everyday occurrence. Few of us stop,
however, to puzzle why bubbling
action takes this form.
Some elementary physical chemistry considerations lead to a solution
to this problem. In forming a bubble,
the steam wishes to expand. The work
it does is the difference in pressure
between the gas inside the bubble and
the water pushing on the bubble multiplied by the volume of the spherical
bubble. A competing process is the
work needed to stretch the bubble skin,
both inside and outside the bubble,
which is given by twice the surface
area of the spherical bubble times the
surface tension. Indeed, the reason
why bubbles are spherical in shape is
that this geometry has the minimum
surface area for a given volume and
thus requires the least amount of work
to maintain its shape.
The actual size of the bubble is
determined by counterbalancing the
rate of change of these two energy
terms as a function of the change in the
radius of the bubble. This analysis 2
tells us that the excess pressure needed
to keep a bubble at a certain size is
proportional to the surface tension and
inversely proportional to the radius of
the bubble. Put into other words, the
smaller the bubble, the larger the
excess pressure needed maintain it.
This conclusion has amusing and
sometimes counterintuitive consequences. Take for example what happens when two balloons, made of the
same material but inflated to different
sizes, are connected to one another by
means of a tube having a closed valve,
as shown in Figure 1a. When the valve
is opened, as shown in Figure 1b, the
pressure equilibrates. But contrary to
the expectations of many, the smaller
balloon becomes smaller and the larger
balloon becomes larger!
continued on page 10
The Nucleus January 2005
9
Bursting Bubbles
Continued from page 9
Figure 1. Two identical balloons
inflated to different sizes and connected by a valve that is closed in (a)
and then opened in (b).
Why does this happen? The
answer is that it is easier to increase
the volume of a larger balloon than a
smaller one, as everyone knows who
has suffered through the initial stages
of inflating a balloon. Thus, to equalize the pressures, the smaller balloon
shrinks while the larger balloon
expands. The above demonstration is
Figure 2. Double bubbles: when a
smaller bubble contacts a larger bubble, the higher pressure of the smaller
bubble causes it to protrude into the
larger one.
10
The Nucleus January 2005
just another illustration of the conclusion: the smaller the bubble is, the
larger must be its internal pressure.
This principle also accounts for
what happens when two bubbles meet
and touch. If the bubbles have the
same size, that is, the same radius and
hence the same excess pressure, then
the interface between the two bubbles
is a flat common wall. But if the bubbles have unequal radii, then the
smaller bubble with the larger pressure
pokes into the larger bubble, causing
the interface to be bent with the
smaller bubble protruding into the
larger one, as shown in Figure 2:
So, how does this concept apply to
boiling a pot of water? When we try to
bring water to a boil, by definition, the
vapor pressure of the water becomes
the same as the outside atmosphere.
But bubbles cannot form in the pure
water. Its surface tension is just too
large, as everyone knows who has tried
to blow bubbles with pure water. To
form a bubble, we need either to
decrease the surface tension, which can
be achieved by adding soap to the
water (and is definitely not recommended for cooking!), or to sequester
the steam bubble from the water that
wants to crush it. This sequestration is
best done in small cavities, nooks, and
crannies that the liquid water cannot
penetrate. Hence imperfections on the
walls of the pot are the place where
bubbles form. These imperfections
cannot be too small because once again
the excess pressure required would be
too large. Indeed, a critical size of the
cavity exists for bubble formation.
Of course, the same concept of a
roughened surface promoting bubble
formation is employed routinely by
chemists when they add boiling chips
to solutions to keep them from bumping when they are heated. Making
phase changes from liquid to gas or
from liquid to solid is notoriously difficult. It explains why in pure water in a
clean, smooth vessel it is easy to superheat the water past its boiling point or
supercool it past its freezing point. We
find ourselves wondering about the
complex phenomenon of nucleation in
causing phase changes to occur.
Although bubbles first sound like
something that is only child’s play,
deeper consideration shows that this
topic has profound aspects. It also has
practical ones, such as how clouds produce rain or snow.
What fun it is to know the science
behind such phenomena. Its realization also gives us a deeper appreciation
of the world and helps us to understand
that science is all about us, not just in
the laboratory. By engaging the audience in a quest to understand various
phenomena involving bubbles in a
“minds-on” if not hands-on manner, it
was hoped that it was possible to validate the last part of the Chinese
proverb: “I do and I understand.”
In closing, if I may be permitted a
few personal observations about the
James Flack Norris Award for Outstanding Achievement in the Teaching
of Chemistry, let me express my profound gratitude and pleasure in being
selected by the Northeastern Section of
the American Chemical Society for
this great honor. Teaching and mentoring are both fairly private activities
whose effectiveness is hard to judge,
even by those most closely associated
with the effort, and often only after the
passage of much time! Yet, it is one of
the most important activities we can do
to renew the love of inquiry and spark
the imagination of the next generation.
I am mindful that many, many others
are qualified – I daresay some more
qualified – to receive this honor, and I
accept it on the behalf of so many of us
whose efforts usually go unmarked and
unsung. This activity is so significant
in preparing future chemists. I am
grateful to the Northeastern Section for
celebrating its importance.
1 For
a wonderful account of bubbleology in a common drink, see the
recently published book, Gérard
Liger-Belair, “Uncorked: The Science
of Champagne,” Princeton University
Press, Princeton, NJ, 2004.
2
In mathematical terms, this balancing
act becomes (d/dr)((4/3)(/r 3 6p))
=(d/dr)(8/r2␴) where r is the radius
of the bubble, 6p is the pressure difference, and ␴ the surface tension. It
follows that 6p = 4␴/r. ◆